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1
2 1. : ( ): : 1
3
4
5 ( )
6 / minimum solar nebula model
7 ( )
8
9
10
11 ( )
12 ( ) SDSS
13 : d 2 r i dt 2 ÿ j i Gm jr ij r 3 ij
14 : : :
15 =
16 Newton
17 3 0.1%
18 19
19 20 20
20 2
21 ( )
22 3 3 (2 )
23 3 3
24 3 2,3
25 20 Figure-8 Solution
26 Figure-8 solution 3 (0.005% )
27
28 d 2 x fpxq (1) dt2 xp0q x 0, dx dt t 0 vp0q v 0 (2)
29 1 dx{dt fpxq xpt ` tq xptq ` tfpxptqq 1
30 1987 2
31 e 2 8.5
32 45 2
33 2009 Nature :
34 Laskar and Gastineau 2009 ( 0.38mm)
35
36
37
38 ( )
39 ( ) )
40 X X
41
42 1
43
44
45 Ill-posed problem??
46
47 :
48
49 fpx, vq : 6 fpx, vqdxdv dxdv
50 Bf Bt ` v f Φ Bf Bv 0, (3) Φ 2 ϕ 4πGρ. (4) G
51 ρ ρ m ż dvf, (5)
52
53 .
54
55 ( ) : ( )
56 ( ) : ( ) ( ) ( )
57 Bv Bt Bρ ` pρvq 0 Bt (6) ` pv qv 1 p Φ ρ (7) 2 Φ 4πGρ (8)
58 ρ: t: v: p: Φ: G:
59 ρ, p, v, Φ ρ ρ 0 ` ρ 1 0 1
60 Bρ 1 Bt ` pρ 0v 1 q ` pρ 1 v 0 q 0 (9) Bv 1 Bt `pv 0 qv 1`pv 1 qv 0 ρ 1 p 1 0 p 1 Φ ρ 2 1 (10) 0 ρ 0 v s 2 Φ 1 4πGρ 1 (11) ˆdp p 1 ρ 1 v 2 s dρ ρ 1 (12) 0
61 0 Bρ 1 Bt ` ρ 1 pρ 0 v 1 q 0 (13) Bv 1 Bt 1 ρ 0 p 1 Φ 1 (14) 2 ρ 1 B 2 ρ 1 Bt 2 v2 s 2 ρ 1 4πGρ 0 ρ 1 0 (15)
62 2
63 ( ) ρ 1 Ce ipk x ωtq (16) ω 2 v 2 s k2 4πGρ 0 (17) k 2 J 4πGρ 0 v 2 s (18)
64 k ą k J ω k k J ω 0 k ă k J ω (16)
65 1{k J
66 k J : λ J λ J c π Gρ 0 v s (19) : M J v 2 s GM J {λ J M J ( λ J )
67 0 : ( )
68 1996
69
70 M82
71 X NASA Chandra X
72 Ñ Ñ
73 2 2
74 Ó
75 dp dm M 4πr4, (20) dr dm 1 4πr 2 ρ, (21) Mprq r p ρ 1
76 ( ) dp dr ρm r 2 (22) p ρt (23)
77 (3) ρ9r 2 ( ) ( ) r Ñ 8
78 : (D ) : D ( ) 1
79 r, m, t G 1 1{r 1{m r{m 2 ( ) t{m ( )
80
81 D D
82
83
84 Ñ Ñ Ñ Ñ Ñ
85
86 Bf Bt Apfpxqq (24) A f 2 f f 0 pxq Apf 0 pxqq 0 f f 0 ` df df
87 (1) df df
88 (2) : df f 0 df : Bdf Bt Bpdfpxqq (25) Bpαdf 1 pxq ` βdf 2 pxqq αbpdf 1 pxqq ` βbpdf 2 pxqq (26)
89 (3) df 1 df 1 df 1, df 2 df 1 ` df 2
90 λ λdf Bpdfq (27) df e λt df 0
91 λ
92 f 0 f 0 df
93 df
94 , D 1.05 λ:
95 (2), D 10
96 (3), D 100
97 , D 709
98 , D 1000
99 gravothermal instavility V. Antnov (1961) : Hachisu & Sugimoto (1978)
100 Hachisu et al. (1978) : Cohn (1980):
101
102 3
103
104
105 ( )
106
107 : %
108 :
109 1 : (6 ) ( )
110 k ω v s Σ κ ω 2 κ 2 2πGΣ k ` v 2 s k2 (28) :
111 R ΦpRq R Φ eff Φ ` L2 z 2R 2 (29) d 2 R dt 2 dφ eff dr (30) R R 0 ` x d 2 x dt 2 κ2 x (31)
112 κ 2 d2 Φ dr 2 ` 3 R 0 dφ dr (32) ( R R 0 )
113 κ Ω Ω 2 1 dφ R dr κ 2 R 0 dω 2 (33) dr ` 4Ω2 (34) κ Ω 2Ω Ω ă κ ă 2Ω (35)
114 (28) ω 2 v 2 s k2 4πGρ 0 (36) ω 2 κ 2 2πGΣ k ` v 2 s k2 (37)
115 v 2 s k2 4πGρ 0 2πGΣ k 3 = 2 κ 2
116 0 v s 0 0 k crit κ2 2πGΣ ; λ crit 2π k crit 4π2 GΣ κ 2 (38) ( ) : 2
117 k ω κ 2 2πGΣ k ` v 2 s k2 ě 0 (39) v s κ πgσ ą 1 (40) Q v sκ πgσ (41) Toomre Q
118 ( ) Q σ Rκ 3.36GΣ ą 1 (42) σ R (π 3.36)
119 : R
120 3 λ crit λ crit 4π2 GΣ κ 2 (43) 1 λ crit Σ (κ 1 ) Σ λ crit
121 1 0.1 λ crit Q
122 tight winding
123 tight-winding tight winding : ( ) = m pω mωq 2 κ 2 2πGΣ k ` v 2 s k2 (44)
124 tight-winding m 0 mω tight-winding Ω
125 グローバルなスパイラルモード 実際の銀河では 全く tight-winding も局所近似 も成り立たないような大き なスケールでのスパイラル 構造が見つかっている 中間赤外で見える低温のガ スは複雑な構造をもつ 大きなスケールでのスパイ M101 銀河 スピッツアー衛星 ラルアームがあるように見 での赤外線画像 える 多くの銀河についてそういう構造があるように見える
126 ( )
127 ( ) 1. ( Lin-Shu ) 2.
128
129 ( )
130 Q 1 Q
131 Q 90 (Fujii et al, 2011) Q
132 Swing Amplification swing amplification
133 Swing Amplification(2) leading arm ( ) trailing trailing leading trailing
134 Swing Amplification(3) leading arm N
135 Q 1970
136 :
137 Katz and Gunn Cray YMP : 1000
138 Saitoh et al GRAPE-5 1 (!) animation 1 : 1
139 :
140 1 : 4-5 :
141 1-2
142 Saitoh et al
143 Star formation with SPH Large scale structure formation with AMR
144 animation (Baba et al 2009) 1 2
145 SPH Cray XT4 ASURA 10pc (Ð 500pc) 10K (Ð 10 4 K ) 3000M d (Ð 10 5 M d )
146 高分解能モデルと観測
147 低分解能モデルと観測
148
149 2006: Xu et al, Science 311, 54 Nov 2008: Burst of results from VLBA Several data from VERA (Compiled by Dr. Asaki)
150 ( 30km/s)
151
152
153
154 ( ) ( )
155 星のスパイラルの運動 星の運動の円運動からのずれ スパイラルアームは実体 密度波では ない 古い星の平均の円運動からのずれ も結構大きい キロパーセクスケールの構造があ る
156 +
157 : -
158 : -
159 Svensmark 2007 :
160 1.4 ( ) : (???)
161
162 ( )
163 ( )
164 : :
165
166 : ( ) : :
167 : 6-10
168 (Fujii et al. 2010) animation a1 animation a2 animation b1 Stable against radial mode (a1, a2) Spiral arms form They seem to be maintained for very long time
169 : ( )
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1. 2. 3. 4. 5. ( ) () http://www-astro.physics.ox.ac.uk/~wjs/apm_grey.gif http://antwrp.gsfc.nasa.gov/apod/ap950917.html ( ) SDSS : d 2 r i dt 2 = Gm jr ij j i rij 3 = Newton 3 0.1% 19 20 20 2 ( ) 3 3
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1 1 ϕ ϕ ϕ S F F = ϕ (1) S 1: F 1 1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l : l r δr θ πrδr δf (1) (5) δf = ϕ πrδr
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